Question

The operation *is defined by x*y=2x-y,where x and y are real numbers.Find the value of (i) y,if y *(3*y)=6​

Answer 1

The value of y = 4

Explanation:

Explanation:-

Given the operation *is defined by

x*y=2 x-y,where x and y are real numbers

Given y * ( 3 * y ) = 6

⇒ y * ( 2 (3) -y) = 6 (∵ x*y=2 x-y)

⇒ y * ( 6 - y) = 6

⇒ 2 (y) - (6 - y ) = 6

⇒ 2 y - 6 + y = 6

⇒ 3 y = 6 + 6

⇒ 3 y = 12

⇒ y = 4

Verification:-

Put y =4 in given operation

L.H.S

y * ( 3 * y ) = 4 * ( 3 * 4)

= 4 * (2(3)-4) (∵ x*y=2 x-y )

= 4 * ( 6-4)

= 4 * 2

= 2(4) -2 (∵ x*y=2 x-y )

= 6

=R.H.S

y *(3*y) = 6​

∴ y = 4 is satisfied